Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on Squares and triangles.
Squares and triangles – AIME I, 1999
The two squares share the same centre O and have sides of length 1, The length of AB is \(\frac{43}{99}\) and the area of octagon ABCDEFGH is \(\frac{m}{n}\) where m and n are relatively prime positive integers, find m+n.
- is 107
- is 185
- is 840
- cannot be determined from the given information
Key Concepts
Squares
Triangles
Algebra
Check the Answer
Answer: is 185.
AIME I, 1999, Question 4
Geometry Vol I to IV by Hall and Stevens
Try with Hints
Triangle AOB, triangleBOC, triangleCOD, triangleDOE, triangleEOF, triangleFOG, triangleGOH, triangleHOA are congruent triangles
with each area =\(\frac{\frac{43}{99} \times \frac{1}{2}}{2}\)
then the area of all 8 of them is (8)\(\frac{\frac{43}{99} \times \frac{1}{2}}{2}\)=\(\frac{86}{99}\) then 86+99=185.
Other useful links
- https://www.cheenta.com/rational-number-and-integer-prmo-2019-question-9/
- https://www.youtube.com/watch?v=lBPFR9xequA